A

solvable group has a subnormal series of subgroups.

by [5], A5 is the smallest non abelian simple group of order 22 .3.5 and the smallest non

solvable group containing four conjugacy classes.

[Abels:1971] Abels Herbert, 1971, An example of a finitely presented

solvable group, London Mathematical Society lecture notes, Cambridge: Cambridge University Press, pp.

any closed, undistorted subgroup (e.g., cocompact lattice) of a direct product of a p-adic

solvable group with a connected, solvable Lie group.

Tessera, see Theorem 4.3 shows that there exists a

solvable group [GAMMA] such that W([GAMMA]) contains S[L.sub.3](Z).

A long standing open problem in the character theory of finite

solvable groups is whether the derived length dl(G) of a

solvable group G is bounded above by the cardinality of cd(G), the set of irreducible character degrees of that group, i.e.

We begin by proving that the generalized free product of a nilpotent group and a

solvable group is not necessarily perfect.

Here we recall that every binary

solvable group except [Q.sub.8] (the group of quaternions) has been proved to be symmetrically sequenceable in [2].

And for a general connected

solvable group S, the Lie subalgebra t [intersection] [s, s] is always central in s.

Let G be a

solvable group in which [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], for 1 [less than or equal to] [[alpha].sub.1] [less than or equal to] [[alpha].sub.2], p a prime and [absolute value of G:C] a prime.

Let G be a

solvable group, then one of the following holds.

One may extend the definition of isotropic torus to the case of

solvable groups as follows.